Alvarus, Thomas
,
Liber de triplici motu
,
1509
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81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
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191 - 200
201 - 210
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Secunde partis
"
file
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0053
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n
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53
"/>
<
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<
s
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xml:space
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preserve
">Quarta ſuppoſitio. </
s
>
<
s
xml:id
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N152B9
"
xml:space
="
preserve
">Diminuere ꝓ-
<
lb
/>
portionē maioris ineq̈litatꝪ eſt ab ea demere ali-
<
lb
/>
quã ꝓportionē maioris inequalitatis ceteris pa-
<
lb
/>
ribus. </
s
>
<
s
xml:id
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N152C2
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xml:space
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preserve
">Et hec diffinitio eſt. </
s
>
<
s
xml:id
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N152C5
"
xml:space
="
preserve
">Contingit autē tot mo-
<
lb
/>
dis proportionē maioris inequalitatis diminui:
<
lb
/>
quot modis ipſam contingit augeri: de quibus in
<
lb
/>
prima ſuppoſitione.</
s
>
</
p
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<
p
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<
s
xml:id
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xml:space
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">Quinta ſuppoſitio. </
s
>
<
s
xml:id
="
N152D2
"
xml:space
="
preserve
">Sēper plus di-
<
lb
/>
minuitur ꝓportio maioris īequalitatis per aug-
<
lb
/>
mentū minoris termini maiore nõ variato: quam
<
lb
/>
per equale decrementū maioris minore nõ varia-
<
lb
/>
to ceteris paribus. </
s
>
<
s
xml:id
="
N152DD
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xml:space
="
preserve
">Et ſemper plus creſcit ꝓpor-
<
lb
/>
tio per decrementū minoris termini: quã ꝑ equa-
<
lb
/>
augmentū maioris ceteris paribꝰ. </
s
>
<
s
xml:id
="
N152E4
"
xml:space
="
preserve
">Prima pars
<
lb
/>
huius ſuppoſitionis probatur: ſit vna ꝓportio f.
<
lb
/>
inter a maiorē terminū et b. minorem. </
s
>
<
s
xml:id
="
N152EB
"
xml:space
="
preserve
">et perdat a.
<
lb
/>
terminus aliquã partē ſui manente b. inuariato:
<
lb
/>
tunc dico / ſi a: nichil deperderet: et b. acquireret
<
lb
/>
tantã partē quantã iam deperdit a. ceteris pari-
<
lb
/>
bus: maiorē ꝓportionē deꝑderet f. ꝓportio quam
<
lb
/>
iam deperdit. </
s
>
<
s
xml:id
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N152F8
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xml:space
="
preserve
">Quod ꝓbatur ſic: q2 b. per acquiſi-
<
lb
/>
tionē illiꝰ partis maiorē ꝓportionē acquirit quã
<
lb
/>
deꝑdat a: ꝑ deperditionē eiuſdē partis vel equa-
<
lb
/>
lis: quod patet: q2 ſi tam a. quã b. deperderent illã
<
lb
/>
partē: maiorē ꝓportionē deperderet b. quam a. / vt
<
lb
/>
patet ex octaua ſuppoſitione quarti capitis huiꝰ
<
lb
/>
partis: igitur quando b. acquirit illam partē et a.
<
lb
/>
deperdit illam: maiorē ꝓportione acquirit b. quã
<
lb
/>
deperdat a. </
s
>
<
s
xml:id
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N1530B
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xml:space
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preserve
">(Suppono em̄ / ſemꝑ a. maneat ma
<
lb
/>
ius) / et ex conſequenti ſequitur / maiorē ꝓportio-
<
lb
/>
nem perdit f. / per augmentū minoris termini pu-
<
lb
/>
ta b. / quã per equale decrementū maioris puta a. /
<
lb
/>
quod fuit ꝓbandū. </
s
>
<
s
xml:id
="
N15316
"
xml:space
="
preserve
">Patet hec cõſequētia / quoniã
<
lb
/>
ſemper ꝓportio inter aliqua duo īequalia perdit
<
lb
/>
illã ꝓportionē quã acquirit minꝰ extremū: et etiã
<
lb
/>
illam quã deperdit maius extremū ceteris paribꝰ /
<
lb
/>
vt patet ex ꝓbationibus none et decime ſuppoſi-
<
lb
/>
tionū ſecundi capitis huius. </
s
>
<
s
xml:id
="
N15323
"
xml:space
="
preserve
">Patet igitur prima
<
lb
/>
pars. </
s
>
<
s
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"
xml:space
="
preserve
">Et eodem modo demonſtrabis ſecundam
<
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/>
</
s
>
<
s
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xml:space
="
preserve
">Intelligo / ſemper maior terminus maior ma-
<
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/>
neat. </
s
>
<
s
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xml:space
="
preserve
">Alias denmõſtratio nõ ꝓcederet.
<
note
position
="
left
"
xlink:href
="
note-0053-01a
"
xlink:label
="
note-0053-01
"
xml:id
="
N1537E
"
xml:space
="
preserve
">1. correĺ.</
note
>
</
s
>
<
s
xml:id
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N15339
"
xml:space
="
preserve
">¶ Ex quo
<
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ſequitur / aliquando tantū diminuitur ꝓportio
<
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/>
maioris inequalitais per crementū minoris nu-
<
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/>
meri adequate ceteris paribus: quantū diminui-
<
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/>
tur per equale decrementū maioris numeri. </
s
>
<
s
xml:id
="
N15344
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xml:space
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preserve
">Pro
<
lb
/>
batur: et volo / ſit vna ꝓportio inter quadrupe-
<
lb
/>
dale et octupedale manente quadrupedali in-
<
lb
/>
uariato octupedale ꝑdat quadrupedale adequa-
<
lb
/>
te: et ſequitur / illa proportio diminuitur vſ ad
<
lb
/>
ꝓportionē equalitatis: volo igitur iterū / manē
<
lb
/>
te octupedali inuariato: quadrupedale acquirat
<
lb
/>
ſupra ſe quadrupedale adequate: et ſequit̄̄ / tunc
<
lb
/>
etiã diminuitur proportio dupla vſ ad propor-
<
lb
/>
tionē equalitatis: igitur correlariū verū
<
note
position
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left
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xlink:href
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note-0053-02a
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note-0053-02
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xml:id
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xml:space
="
preserve
">2. correĺ.</
note
>
</
s
>
<
s
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xml:space
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">¶ Sequi
<
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/>
tur ſecūdo / per equale decrementū maioris ter-
<
lb
/>
mini et ſimul equale crementū minoris proportio
<
lb
/>
manet equalis. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">Patet correlariū poſito / octu-
<
lb
/>
pedale a. deperdat quadrupedale: et quadrupeda
<
lb
/>
le b. acquirat tantū puta quadrupedale. </
s
>
<
s
xml:id
="
N1536E
"
xml:space
="
preserve
">quo poſi
<
lb
/>
to ſequitur / in fine inter illos terminos erit pro
<
lb
/>
portio dupla ſicut erat in principio. </
s
>
<
s
xml:id
="
N15375
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xml:space
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preserve
">Nã in fine b.
<
lb
/>
erit octupedale a. vero quadrupedale: igitur.</
s
>
</
p
>
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p
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<
s
xml:id
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xml:space
="
preserve
">His iactis ſit prima concluſio. </
s
>
<
s
xml:id
="
N1538E
"
xml:space
="
preserve
">Si
<
lb
/>
vtra duaꝝ latitudinū inequaliū vniformiter cõ-
<
lb
/>
tinuo diminuatur ſiue in tēpore equali ſiue ineq̈li
<
lb
/>
ꝑdendo equalē latitudinē oīno: maiorē ꝓportionē
<
lb
/>
deꝑdet minor latitudo quã maior: hoc eſt īter ipſã
<
cb
chead
="
Capitulum octauū.
"/>
minorē latitudinem in principio diminutionis et
<
lb
/>
ſeipſam in fine erit maior ꝓportio quã inter alte-
<
lb
/>
ram maiorē latitudinē in principio et ſeipſam in
<
lb
/>
fine. </
s
>
<
s
xml:id
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xml:space
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">Exēplū / vt captis duabus latitudinibus puta
<
lb
/>
pedali et bipedali ſiue vniꝰ gradꝰ et duoꝝ graduū
<
lb
/>
(nõ eſt cura:) ſi latitudo pedalis ꝑdat in hora vni-
<
lb
/>
formiṫ ſemipedale: et latitudo bipedalis in tãto
<
lb
/>
tēpore vel maiore vel minori </
s
>
<
s
xml:id
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N153AD
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xml:space
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preserve
">(Non īpedit ꝓpoſi-
<
lb
/>
tum) perdat vniformiter ſemipedale adequate:
<
lb
/>
maiorē ꝓportionē deperdit pedale quã ſemipeda
<
lb
/>
le: qm̄ inter pedale in principio et ſeipſum in fine
<
lb
/>
eſt ꝓportio dupla: inter bipedale vero in prīcipio
<
lb
/>
et ſeipſum in fine eſt ꝓportio ſexquialtera. </
s
>
<
s
xml:id
="
N153BA
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xml:space
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">Pro-
<
lb
/>
batur hoc cõcluſio facile: qm̄ quandocun latitu-
<
lb
/>
do maior et minor equalē partē ſiue exceſſū ſiue la
<
lb
/>
titudinē deperdūt: maiorē ꝓportionē deperdit la
<
lb
/>
titudo minor quã maior: vt ptꝫ manifeſte ex octa-
<
lb
/>
ua ſuppoſitione quarti capitis huiꝰ partis: igit̄̄
<
lb
/>
concluſio vera.
<
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right
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note-0053-03a
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note-0053-03
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xml:id
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xml:space
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">1. correĺ.</
note
>
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